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Lobachevskii Journal of Mathematics

Partial Discrimination Between Mixed States and Eavesdropping Strategy for Symmetric Coherent States Quantum Cryptography

Dmitry Anatolevich Kronberg

Published Jun 1, 2026• 0 citations
Publisher

Abstract

Abstract Quantum cryptography uses non-orthogonal quantum states, and the eavesdropper cannot extract full information without being detected. Nevertheless, losses in fiber channels allow for additional eavesdropping strategies based on postselective measurements. Here, we study the strategy based on unambiguous discrimination between mixed quantum states, and its partial version with higher success probability. We find information available to the eavesdropper for two protocols of quantum key distribution, namely, geometrically uniform states and subcarrier wave protocols.

DOI
10.1134/s1995080226618643

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Abstract Quantum cryptography uses non-orthogonal quantum states, and the eavesdropper cannot extract full information without being detected. Nevertheless, losses in fiber channels allow for additional eavesdropping strategies based on postselective measurements. Here, we study the strategy based on unambiguous discrimination between mixed quantum states, and its partial version with higher success probability. We find information available to the eavesdropper for two protocols of quantum key distribution, namely, geometrically uniform states and subcarrier wave protocols.
Abstract Symmetric coherent states are of interest in quantum cryptography, since for such states there is an upper bound for unambiguous state discrimination (USD) probability, which is used to resist USD attack. But it is not completely clear what an eavesdropper can do for shorter channel length, when USD attack in not available. We consider the task of generalized discrimination between symmetric coherent states and construct an operation which enlarges the information content of the states with fixed failure probability. We apply this transformation to develop a zero-error eavesdropping strategy for quantum cryptography on symmetric coherent states.
Abstract Quantum key distribution (QKD) is a quantum technology which creates a common secret key between two distant users without any technological and computational assumptions about the eavesdropper. Nevertheless, not all the QKD protocols have tight upper and lower security bounds, thus the study of eavesdropping strategies and countermeasures is important. Using large number of symmetric coherent states is one of possible technologies in quantum key distribution against unambiguous state discrimination (USD) attack. Here we propose an attack based on heterodyne measurement, which is relatively simple for practical implementation and which becomes more powerful than USD attack when the number of states in the protocol is large enough. We study the performance of this attack for various symmetric coherent states QKD protocol parameters and for various distances between the legitimate users.
The safety of a quantum key distribution system relies on the fact that any eavesdropping attempt on the quantum channel creates errors in the transmission. For a given error rate, the amount of information that may have leaked to the eavesdropper depends on both the particular system and the eavesdropping strategy. In this work, we discuss quantum cryptographic protocols based on the transmission of weak coherent states and present a new system, based on a symbiosis of two existing ones, and for which the information available to the eavesdropper is significantly reduced. This system is therefore safer than the two previous ones. We also suggest a possible 1 experimental implementation.
Abstract The quantum key distribution protocol utilizing 8 geometrically uniform coherent states is considered. We analyze its security against a generalized photon-number-splitting attack. This protocol allows for several basis configurations, and we demonstrate that one of these configurations is more vulnerable. We also use the previously described methods for attack improvement, namely, modification of observable’s coefficients and using extra photon as assistance for increasing success probability.
Purpose of work is to review new aspects for the task of information extraction from ensembles of quantum states, dictated by practical tasks of quantum cryptography. Research methods: mathematical methods of quantum information theory, in particular, unambiguous discrimination of quantum states. Results of the study: the paper analyzes the literature on the topic of eavesdropper information bounds in quantum cryptography in the presence of channel attenuation, including in the absence of quantum memory. The features of application of the fundamental information bound to the eavesdropper information in the presence of attenuation, the threats of application of ad hoc countermeasures for unambiguous state discrimination attack are demonstrated. The problems of finding an effective postselective eavesdropping transformation, as well as measurement in the absence of eavesdropper’s quantum memory, are formulated. Scientific novelty: the scientific novelty consists in the integration of disparate approaches to the problem of eavesdropper information bounds in quantum cryptography and resisting attacks in case of lossy channel. The review describes the peculiarities of applying information bound to quantum cryptography problems and formalizes the challenges facing the eavesdropper under attenuation conditions.
It is shown that the quantum cryptography protocol on geometrically uniform coherent states, which uses the restriction for unambiguous discrimination of a set of symmetric coherent states and allows resisting an unambiguous state discrimination attack (USD attack), is not secure to a number of other attacks. The key length formula from the work of S.N. Molotkov [ JETP Lett. , 101 (8), 579 (2015) ] and the key generation rate for a number of constructive attacks of the eavesdropper are compared and it is shown that the key generation rate in this work is significantly overestimated. This leads to the fact that the distributed key is not secret.